Reply to: "Man vs. Machine Learning Revisited"

Abstract

In their reexamination of Binsbergen et al. (2023) [BHL], Zhang et al. (2025) [ZZL] correctly identify a look-ahead bias (data leakage) in certain forecast horizons of BHL’s earnings forecasts. We acknowledge and correct this issue. Using the replication code provided by ZZL, we compare the corrected implementation of BHL with ZZL’s results and confirm that the two implementations produce consistent findings.

We then show that ZZL’s two central claims are not supported by their own empirical results. First, they claim that abnormal return predictability disappears after correcting for the data leakage problem. Second, they argue that linear models perform as well as machine-learning models when forecasting earnings.

With respect to return predictability, ZZL’s own results and code show that the CAPM and Fama–French three-factor alphas remain economically large (-0.68% and -0.77% per month, respectively) and highly statistically significant after correcting for the look-ahead bias. While the Fama–French five-factor (FF5) alpha reported in the published version of ZZL is marginally insignificant, we show that using updated CRSP and Fama–French factor data over the same sample period increases the FF5 alpha to -0.48% per month (-5.8% per year), restoring statistical significance. Moreover, we show that a volatility-managed version of the strategy, which scales returns based on conditional volatility, delivers economically meaningful and statistically significant returns and alphas across a large number of factor specifications, including FF5. These findings indicate that cross-sectional return predictability remains robust after correcting for the data leakage identified by ZZL. There was already agreement with ZZL that the other results in BHL remain intact after the correction.

With respect to forecasting performance, ZZL’s proposed linear models rely on retrospective variable selection and therefore have their own form of forward-looking bias. Even with this advantage, the linear models exhibit higher mean squared errors than the machine-learning methods across most forecast horizons. When restricting the information set to the same forecasting variables used in ZZL’s linear models, machine-learning methods outperform linear models across all five forecast horizons and statistically significantly so in four of the five. When the variable selection bias is removed by considering a broader set of signals, the performance gap widens further, highlighting the importance of nonlinearities for accurate forecasting.

In summary, the corrected evidence confirms that the conclusions of BHL remain fully intact: machine-learning models provide superior forecasts relative to both analysts and linear models, and conditional biases remain strongly associated with cross-sectional return predictability.